Experimental evidence of size-selective harvest and environmental stochasticity effects on population demography,fluctuations and non-linearity

Theory and analyses of fisheries data sets indicate that harvesting can alter population structure and destabilise non-linear processes, which increases population fluctuations. We conducted a factorial experiment on the population dynamics of Daphnia magna in relation to size-selective harvesting and stochasticity of food supply. Harvesting and stochasticity treatments both increased population fluctuations. Timeseries analysis indicated that fluctuations in control populations were non-linear, and non-linearity increased substantially in response to harvesting. Both harvesting and stochasticity induced population juvenescence, but harvesting did so via the depletion of adults, whereas stochasticity increased the abundance of juveniles. A fitted fisheries model indicated that harvesting shifted populations towards higher reproductive rates and larger-magnitude damped oscillations that amplify demographic noise. These findings provide experimental evidence that harvesting increases the non-linearity of population fluctuations and that both harvesting and stochasticity increase population variability and juvenescence.     

Estimating the growth of a newly established moose population using reproductive value

Estimating the population growth rate and environmental stochasticity of long-lived species is difficult because annual variation in population size is influenced by temporal autocorrelations caused by fluctuations in the age-structure. Here we use the dynamics of the reproductive value to estimate the long-term growth rate s and the environmental variance of a moose population that recently colonized the island of Vega in northern Norway. We show that the population growth rate was high (ŝ=0.26). The major stochastic influences on the population dynamics were due to demographic stochasticity, whereas the environmental variance was not significantly different from 0. This supports the suggestion that population growth rates of polytocous ungulates are high, and that demographic stochasticity must be assessed when estimating the growth of small ungulate populations.     

Effects on population persistence: the interaction between environmental noise colour,intraspecific competition and space

It is accepted that accurate estimation of risk of population extinction, or persistence time, requires prediction of the effect of fluctuations in the environment on population dynamics. Generally, the greater the magnitude, or variance, of environmental stochasticity, the greater the risk of population extinction. Another characteristic of environmental stochasticity, its colour, has been found to affect population persistence. This is important because real environmental variables, such as temperature, are reddened or positively temporally autocorrelated. However, recent work has disagreed about the effect of reddening environmental stochasticity. Ripa and Lundberg (1996) found increasing temporal autocorrelation (reddening) decreased the risk of extinction, whereas a simple and powerful intuitive argument (Lawton 1988) predicts increased risk of extinction with reddening. This study resolves the apparent contradiction, in two ways, first, by altering the dynamic behaviour of the population models. Overcompensatory dynamics result in persistence times increasing with increased temporal autocorrelation; undercompensatory dynamics result in persistence times decreasing with increased temporal autocorrelation. Secondly, in a spatially subdivided population, with a reasonable degree of spatial heterogeneity in patch quality, increasing temporal autocorrelation in the environment results in decreasing persistence time for both types of competition. Thus, the inclusion of coloured noise into ecological models can have subtle interactions with population dynamics.     

种群统计随机性和环境随机性对种群绝灭的影响

影响种群绝灭的随机干扰可分为种群统计随机性、环境随机性和随机灾害三大类。在相对稳定的环境条件下和相对较短的时间内,以前两类随机干扰对种群绝灭的影响为生态学家关注的焦点。但是,由于自然种群动态及其影响因子的复杂特征,进一步深入研究随机干扰对种群绝灭的作用在理论上和实践上都必须发展新的技术手段。本文回顾了种群统计随机性与环境随机性的概念起源与发展,系统阐述了其分析方法。归纳了两类随机性在种群绝灭研究中的应用范围、作用方式和特点的异同和区别方法。各类随机作用与种群动态之间关系的理论研究与对种群绝灭机理的实践研究紧密相关。根据理论模型模拟和自然种群实际分析两方面的研究现状,作者提出了进一步深入研究随机作用与种群非线性动态方法的策略。指出了随机干扰影响种群绝灭过程的研究的方向：更多的研究将从单纯的定性分析随机干扰对种群动力学简单性质的作用,转向结合特定的种群非线性动态特征和各类随机力作用特点具体分析绝灭极端动态的成因,以期做出精确的预测。     

Predicting the time to quasi-extinction for populations far below their carrying capacity

Populations threatened by extinction are often far below their carrying capacity. A population collapse or quasi-extinction is defined to occur when the population size reaches some given lower density. If this density is chosen to be large enough for the demographic stochasticity to be ignored compared to environmental stochasticity, then the logarithm of the population size may be modelled by a Brownian motion until quasi-extinction occurs. The normal-gamma mixture of inverse Gaussian distributions can then be applied to define prediction intervals for the time to quasi-extinction in such processes. A similar mixture is used to predict the population size at a finite time for the same process provided that quasi-extinction has not occurred before that time. Stochastic simulations indicate that the coverage of the prediction interval is very close to the probability calculated theoretically. As an illustration, the method is applied to predict the time to extinction of a declining population of white stork in southwestern Germany.     

Effective size of a fluctuating age-structured population

Previous theories on the effective size of age-structured populations assumed a constant environment and, usually, a constant population size and age structure. We derive formulas for the variance effective size of populations subject to fluctuations in age structure and total population size produced by a combination of demographic and environmental stochasticity. Haploid and monoecious or dioecious diploid populations are analyzed. Recent results from stochastic demography are employed to derive a two-dimensional diffusion approximation for the joint dynamics of the total population size, N, and the frequency of a selectively neutral allele, p. The infinitesimal variance for p, multiplied by the generation time, yields an expression for the effective population size per generation. This depends on the current value of N, the generation time, demographic stochasticity, and genetic stochasticity due to Mendelian segregation, but is independent of environmental stochasticity. A formula for the effective population size over longer time intervals incorporates deterministic growth and environmental stochasticity to account for changes in N.     

Demographic factors and genetic variation influence population persistence under environmental change

Population persistence has been studied in a conservation context to predict the fate of small or declining populations. Persistence models have explored effects on extinction of random demographic and environmental fluctuations, but in the face of directional environmental change they should also integrate factors affecting whether a population can adapt. Here, we examine the population‐size dependence of demographic and genetic factors and their likely contributions to extinction time under scenarios of environmental change. Parameter estimates were derived from experimental populations of the rainforest species, Drosophila birchii, held in the lab for 10 generations at census sizes of 20, 100 and 1000, and later exposed to five generations of heat‐knockdown selection. Under a model of directional change in the thermal environment, rapid extinction of populations of size 20 was caused by a combination of low growth rate (r) and high stochasticity in r. Populations of 100 had significantly higher reproductive output, lower stochasticity in r and more additive genetic variance (V_A) than populations of 20, but they were predicted to persist less well than the largest size class. Even populations of 1000 persisted only a few hundred generations under realistic estimates of environmental change because of low V_A for heat‐knockdown resistance. The experimental results document population‐size dependence of demographic and adaptability factors. The simulations illustrate a threshold influence of demographic factors on population persistence, while genetic variance has a more elastic impact on persistence under environmental change.     

Causes and consequences of small population size for a specialist parasitoid wasp

The parasitoid wasp Cotesia melitaearum lives in extremely small extinction-prone populations in the Åland islands of southwest Finland. Intensive observational data from two generations, a laboratory competition experiment, and 8 years of survey data were used to measure the causes, extent and consequences of small population size for this parasitoid. In the spring generations of 1999 and of 2000 we observed 21 out of 23 and 26 populations respectively, ranging in size from 2 to 103 parasitoid cocoons. Within these populations the fraction of individuals surviving to adulthood decreased with increasing parasitoid population size. The largest source of mortality was predation (44%) followed by parasitism (20%) and unknown causes (10%). In the field about 30% of the host butterfly larvae are parasitized by a competing parasitoid, Hyposoter horticola. A laboratory competition experiment showed that C. melitaearum eggs died when laid in post-diapause host larvae occupied by H. horticola. Consequently one-third of the progeny of the over-wintering generation of C. melitaearum from the field die as a result of larval competition. The survey of host and parasitoid population dynamics over 8 years showed that extinction of local host butterfly populations occupied by the parasitoid was not associated with current parasitoid population size. Over the same period small parasitoid populations were more likely to become extinct than large populations. However, parasitoid population size was not related to parasitoid extinction when the host also became extinct. These data suggest that the parasitoid populations are kept small through the action of natural enemies and competitors, some of which are density dependent. Local populations are so small that they become extinct frequently and rarely measurably affect the population dynamics of their host. It is likely that this parasitoid persists in Åland because of the spatial asynchrony of local population dynamics.     

Interspecific differences in stochastic population dynamics explains variation in Taylor's temporal power law

Taylor’s power law, i.e. that the slope for the increase in variance with mean population size is between 1 and 2 at a logarithmic scale, provides one of the few quantitative relationships in population ecology, yet the underlying ecological mechanisms are only poorly understood. Stochastic theory of population dynamics predicts that demographic and environmental stochasticity will affect the slope differently. In a stable environment under the influence of demographic stochasticity alone the slope will be equal to 1. In large populations in which demographic variance will have a negligible effect on the dynamics the slope will approach 2. In addition, the slope will also be influenced by how the strength of density dependence is related to mean population size. To disentangle the relative contribution of these processes we estimate the mean‐variance relationship for a large number of populations of British birds. The variance in population size of most species decreased with the mean due to decreased influence of demographic stochasticity at larger population sizes. Interspecific differences in demographic stochasticity was the main factor influencing variation in slopes of Taylor’s power law among species through a significant negative relationship between the slope and demographic variance. In addition, slopes were influenced by interspecific variation in life history parameters such as adult survival and clutch size. These analyses show that Taylor’s power law is generated from an interplay between stochastic and density dependent factors, modulated by life history.     

Effect of population size on the prospect of species survival

Many recent studies have demonstrated a negative effect of small population size on single plant traits. However, not much is known about the actual consequences of reduced plant performance on the long-term prospect of species survival. I studied the effect of population size on population growth rate and survival probability in the rare perennial herbScorzonera hispanica occurring in fragmented grasslands. Its performance was measured using several traits related to reproduction in 21 populations ranging in size from 3 to 2475 plants. These data were then connected with data on full demography of the species from three of the studied populations. Two different matrix models differing in the number of transitions based on measurements in the populations differing in size were used to explore the relationship between population size and population growth rate. Both matrix models showed that despite the decline in seed production in small populations, population growth rate is never significantly different from one, and the populations could thus be expected to survive in the long run. Calculations of extinction probabilities that take into account demographic and environmental stochasticity, however, showed that populations below 100 flowering individuals have a high probability to become extinct. This demonstrates that demographic and environmental stochasticity is an important driver of the fate of small populations in this system. This study demonstrates that estimation of population growth rate can provide new insights into the effect of population size on population growth and survival. It also shows how matrix models enable the combination various pieces of information about the single populations into one overall measure, and may provide a useful tool for the standardization of studies on the effects of population size on population performance.     

Local and Regional Determinants of Colonisation-Extinction Dynamics of a Riparian Mainland-Island Root Vole Metapopulation

The role of local habitat geometry (habitat area and isolation) in predicting species distribution has become an increasingly more important issue, because habitat loss and fragmentation cause species range contraction and extinction. However, it has also become clear that other factors, in particular regional factors (environmental stochasticity and regional population dynamics), should be taken into account when predicting colonisation and extinction. In a live trapping study of a mainland-island metapopulation of the root vole (Microtus oeconomus) we found extensive occupancy dynamics across 15 riparian islands, but yet an overall balance between colonisation and extinction over 4 years. The 54 live trapping surveys conducted over 13 seasons revealed imperfect detection and proxies of population density had to be included in robust design, multi-season occupancy models to achieve unbiased rate estimates. Island colonisation probability was parsimoniously predicted by the multi-annual density fluctuations of the regional mainland population and local island habitat quality, while extinction probability was predicted by island population density and the level of the recent flooding events (the latter being the main regionalized disturbance regime in the study system). Island size and isolation had no additional predictive power and thus such local geometric habitat characteristics may be overrated as predictors of vole habitat occupancy relative to measures of local habitat quality. Our results suggest also that dynamic features of the larger region and/or the metapopulation as a whole, owing to spatially correlated environmental stochasticity and/or biotic interactions, may rule the colonisation – extinction dynamics of boreal vole metapopulations. Due to high capacities for dispersal and habitat tracking voles originating from large source populations can rapidly colonise remote and small high quality habitat patches and re-establish populations that have gone extinct due to demographic (small population size) and environmental stochasticity (e.g. extreme climate events).     

The diversity of population responses to environmental change

The current extinction and climate change crises pressure us to predict population dynamics with ever‐greater accuracy. Although predictions rest on the well‐advanced theory of age‐structured populations, two key issues remain poorly explored. Specifically, how the age‐dependency in demographic rates and the year‐to‐year interactions between survival and fecundity affect stochastic population growth rates. We use inference, simulations and mathematical derivations to explore how environmental perturbations determine population growth rates for populations with different age‐specific demographic rates and when ages are reduced to stages. We find that stage‐ vs. age‐based models can produce markedly divergent stochastic population growth rates. The differences are most pronounced when there are survival‐fecundity‐trade‐offs, which reduce the variance in the population growth rate. Finally, the expected value and variance of the stochastic growth rates of populations with different age‐specific demographic rates can diverge to the extent that, while some populations may thrive, others will inevitably go extinct.     

Life history variation between species of the relictual genus Borderea (Dioscoreaceae): phylogeography, genetic diversity, and population genetic structure assessed by RAPD markers

The genus Borderea consists of two species, B. pyrenaica and B. chouardii, taxa which have been previously considered as conspecific due to their overall close morphology. These two sole species of the rare genus of Dioscoreaceae are endemic to the Pyrenees (Spain, France). This mountain range likely operated as a refugium for these plants during the last glaciations. B. chouardii is only known from a single population in the Spanish Prepyrenees and has been classified as at risk of extinction in the Red List of Endangered Species (IUCN); B. pyrenaica shows a narrow distribution range in the central Pyrenees and Prepyrenees. We analysed genetic variation, population structure and differentiation in these two taxa using RAPD markers. Our study was conducted on the same seven populations for which very low levels of genetic differentiation were detected previously through allozyme analysis. By contrast, high levels of genetic variability were detected through the RAPD hypervariable markers. Twelve RAPD primers produced 112 distinct bands in the 397 surveyed individuals, totalling 395 different RAPD phenotypes. Only four bands were monomorphic across all samples of Borderea, whereas 21 of the polymorphic bands were species‐specific (20 for B. chouardii, and one for B. pyrenaica). The largest genetic distances were those between the B. chouardii and the B. pyrenaica phenotypes. An analysis of molecular variance showed greater variance between groups (B. chouardii vs. B. pyrenaica, 76.08%) than within groups (3.60%). RAPD band specificity, phenotypic distances, and the partitioning of variance all support the taxonomic separation of the two species. Statistical evaluation of within‐ and among‐population RAPD genetic variability in B. pyrenaica showed that genetic variability was higher within populations (>80%) than among them. No clear pattern of RAPD differentiation could be observed among the six studied populations of this taxon though slight differences in genetic diversity could be observed in the more isolated Prepyrenean populations compared with the more widespread Pyrenean ones. These results suggest a recent postglacial origin of the present B. pyrenaica populations. © 2003 The Linnean Society of London, Biological Journal of the Linnean Society, 2003, 80 , 483–498.     

Relatedness and competitive asymmetry – implications for growth and population dynamics

The members of natural populations often differ in size and relatedness to each other, which may affect the division of limited resources and have consequences on reproductive success and population dynamics. We modeled seasonal growth and dynamics in populations composed of different types of relatives (full-sibs, half-sibs and non-related individuals) under the continuum of competitive scenarios between complete symmetry and asymmetry. Growth was assumed logistic in proportion to individual biomass and the size-differences were weighted by the relatedness of individuals. The symmetric component of competition was experienced by all individuals in proportion to their biomass, whereas the asymmetric component was individual-specific, and influenced only by the individuals larger than the focal individual. Relatedness decreased and competitive asymmetry increased the variability of individual biomasses. Mortality of the smallest individuals and the size threshold of reproduction decreased population density. Population dynamics were stable when there was no size threshold for reproduction but the presence of the threshold led to cyclic dynamics under low competitive asymmetry. The effects of the threshold were greater among related than unrelated individuals. The results suggest that individual differences and the asymmetry of competition can greatly affect population dynamics. Full symmetry of competition may be evolutionarily unstable in populations of related individuals as it may increase the probability of extinction due to demographic stochasticity.     

Climate variation and regional gradients in population dynamics of two hole-nesting passerines

Latitudinal gradients in population dynamics can arise through regional variation in the deterministic components of the population dynamics and the stochastic factors. Here, we demonstrate an increase with latitude in the contribution of a large-scale climate pattern, the North Atlantic Oscillation (NAO), to the fluctuations in size of populations of two European hole-nesting passerine species. However, this influence of climate induced different latitudinal gradients in the population dynamics of the two species. In the great tit the proportion of the variability in the population fluctuations explained by the NAO increased with latitude, showing a larger impact of climate on the population fluctuations of this species at higher latitudes. In contrast, no latitudinal gradient was found in the relative contribution of climate to the variability of the pied flycatcher populations because the total environmental stochasticity increased with latitude. This shows that the population ecological consequences of an expected climate change will depend on how climate affects the environmental stochasticity in the population process. In both species, the effects will be larger in those parts of Europe where large changes in climate are expected.     

Modeling the dynamics of natural rotifer populations: Phase-parametric analysis

A model of the dynamics of natural rotifer populations is described as a discrete non-linear map depending on three parameters, which reflect characteristics of the population and environment. Model dynamics and their change by variation of these parameters were investigated by methods of bifurcation theory. A phase-parametric portrait of the model was constructed and domains of population persistence (stable equilibrium, periodic and a-periodic oscillations of population size) as well as population extinction were identified and investigated. The criteria for population persistence and approaches to determining critical parameter values are described. The results identify parameter values that lead to population extinction under various environmental conditions. They further illustrate that the likelihood of extinction can be substantially increased by small changes in environmental quality, which shifts populations into new dynamical regimes.     

Correlated extinctions, colonizations and population fluctuations in a highly connected ringlet butterfly metapopulation

 The persistence of metapopulations is likely to be highly dependent on whether population dynamics are correlated among habitat patches as a result of migration between patches and spatially-correlated environmental stochasticity (weather effects). We examined whether population dynamics of the ringlet butterfly, Aphantopus hyperantus, were synchronous in an area of approximately 0.5 km², with respect to extinction, colonization and population fluctuations. Monks Wood Butterfly Monitoring Scheme transect count data from 1973 to 1995, revealed (A) a major environmental perturbation, the drought of 1976, which caused synchronized extinctions of A. hyperantus in subsequent years, (B) synchronized recolonization in years following the large number of apparent extinctions, and (C) population changes by A. hyperantus were highly correlated in many of the 14 sections of the transect, presumably reflecting similar responses to environmental stochasticity, and the exchange of individuals among sections. However, extinction and population synchrony depended on habitat type. Following the 1976 drought, A. hyperantus apparently became extinct from the most open and most shady habitats it occupied, with some persistence in habitats of intermediate shading, thus showing retraction to core populations in central parts of an environmental gradient, albeit with an average shift to relatively open habitat. Populations at extreme ends of the environmental gradient occupied by A. hyperantus fluctuated least synchronously, suggesting a potential buffering effect of habitat heterogeneity, but this was not crucial to survival after the 1976 drought. Thus, not all habitats are equally important to persistence. Correlated temporal dynamics, variation in habitat quality and the interaction between habitat quality and temporal environmental stochasticity are important determinants of metapopulation persistence and should be incorporated in metapopulation models. Received: 26 April 1996 / Accepted: 17 July 1996     

Stochastic analogues of deterministic single-species population models

Although single-species deterministic difference equations have long been used in modeling the dynamics of animal populations, little attention has been paid to how stochasticity should be incorporated into these models. By deriving stochastic analogues to difference equations from first principles, we show that the form of these models depends on whether noise in the population process is demographic or environmental. When noise is demographic, we argue that variance around the expectation is proportional to the expectation. When noise is environmental the variance depends in a non-trivial way on how variation enters into model parameters, but we argue that if the environment affects the population multiplicatively then variance is proportional to the square of the expectation. We compare various stochastic analogues of the Ricker map model by fitting them, using maximum likelihood estimation, to data generated from an individual-based model and the weevil data of Utida. Our demographic models are significantly better than our environmental models at fitting noise generated by population processes where noise is mainly demographic. However, the traditionally chosen stochastic analogues to deterministic models--additive normally distributed noise and multiplicative lognormally distributed noise--generally fit all data sets well. Thus, the form of the variance does play a role in the fitting of models to ecological time series, but may not be important in practice as first supposed.     

Allee effects,extinctions, and chaotic transients in simple population models

Discrete time single species models with overcompensating density dependence and an Allee effect due to predator satiation and mating limitation are investigated. The models exhibit four behaviors: persistence for all initial population densities, bistability in which a population persists for intermediate initial densities and otherwise goes extinct, extinction for all initial densities, and essential extinction in which "almost every" initial density leads to extinction. For fast-growing populations, these models show populations can persist at high levels of predation even though lower levels of predation lead to essential extinction. Alternatively, increasing the predator's handling time, the population's carrying capacity, or the likelihood of mating success may lead to essential extinction. In each of these cases, the mechanism behind these disappearances are chaotic dynamics driving populations below a critical threshold determined by the Allee effect. These disappearances are proceeded by chaotic transients that are proven to be approximately exponentially distributed in length and highly sensitive to initial population densities.     

Could parasites destabilize mouse populations? The potential role of Pterygodermatites peromysci in the population dynamics of free-living mice, Peromyscus leucopus

Peromyscus leucopus populations exhibit unstable population dynamics. Mathematical models predict instability with chronic parasite infections that reduce host fecundity when the parasite distribution within the host population is close to random. We examined the role the nematode Pterygodermatites peromysci may play in influencing the dynamics of these mice. There were seven gastrointestinal worms infecting mice. Pterygodermatites peromysci was the most prevalent and varied seasonally from 12.3% in November to 36.0% in July. Prevalence was higher in adults (30.8%) than juveniles (4.6%) and there were no statistical differences in prevalence or intensity between the sexes. Overall the distribution was random; the relationship between log variance and log mean of P. peromysci intensity from 17 sites was not significantly different from unity. There were significant relationships between infection and breeding condition, suggesting parasites could be the cause of reduced female breeding. A generalized linear model found the likelihood of P. peromysci infection in adults increased with body mass, the presence of other helminths, and when hosts were in breeding condition. Likewise, the intensity of infection was positively related to co-infections and body mass. Pterygodermatites peromysci infection was associated with the presence of the oxyurid nematode Syphacia peromysci but co-infection was lower in females than males. Amongst females, co-infection was greater when breeding, particularly during lactation. The P. peromysci age-intensity relationship increased with age and rose to an asymptote as expected for a parasite with constant mortality and no acquired immunity. Overall, P. peromysci had a random distribution and was associated with reduced breeding; we discuss how these destabilizing processes may influence the dynamics of P. leucopus.